Wash the banana, peel it, and mash it with a fork. It's best to use a very ripe banana in this recipe, which will be much sweeter (if you don't use such a banana, you might need to add a bit more sweetener). Wash, peel, and grate the carrot on a coarse grater.
In a bowl, combine the banana, carrot, yogurt, flour, sweetener, and baking powder. Crack the egg into the mixture and mix thoroughly until all ingredients are combined.
Heat a non-stick frying pan over medium heat. Warm and spread small amounts of oil in the pan to fry several pancakes at a time. Scoop out 1 large tablespoon of batter per pancake and smooth them out from the top. Fry all the pancakes until lightly risen and golden, about 2-3 minutes on each side.
Transfer the cooked pancakes onto a plate. Eat warm or cold.